CHICAGO -- Rick Hahn wasn't just escaping the polar vortex when he skipped Wednesday's Hall of Fame celebration for Frank Thomas. If not for the Midwest being dropped into a flight-canceling deep freeze, he would have loved the chance to show Masahiro Tanaka around his hometown and let him get a look at what it would be like to have a locker alongside Chris Sale's in the U.S. Cellular Field clubhouse.

But Hahn, Kenny Williams and Robin Ventura were happy to divert themselves to a Los Angeles hotel to meet with the Japanese ace. Like Cuban slugger Jose Abreu, they believe Tanaka could be an instant changer for an organization that won 22 fewer games in 2013 than the year before, finishing a numbing 30 games behind the Tigers in the AL Central.

In a statement on Thursday, Hahn called the White Sox meeting "exploratory in nature." But while it seems too strong to suggest they are prepared to outbid the Yankees, Dodgers, Diamondbacks and everyone else -- the Cubs included -- their interest goes beyond tire kicking and due diligence.

Hahn, working alongside Williams, the executive vice president who was his predecessor as general manager, has done a remarkable job reshaping the organization over the past nine months. He's taken an old big league roster and a thin farm system and somehow created the same kind of base that existed at the turn of the century, when Paul Konerko, Magglio Ordonez, Carlos Lee and Mark Buehrle were kids.

Beginning with heavy spending in the Draft and the signing of 16-year-old Dominican power hitter Micker Zapata, it's been anything but business as usual for a front office that had lost its team-building mojo. The willingness to bid veterans like Jake Peavy, Alex Rios and A.J. Pierzynski goodbye and the series of smart deals in which Abreu, Avisail Garcia, Adam Eaton and Matt Davidson came aboard -- adding to talent percolating in the rejuvenated farm system -- puts the White Sox in position to compete for Tanaka.

It also helps that Sale is as solid of a team guy as he is a fearsome sight for hitters, especially of the left-handed variety.

Hahn's first good move after taking over as GM was to sign Sale to a five-year, $32.5 million contract last March, just before Sale turned 24. The best part about the deal might be that it includes 2018 and '19 club options at team-friendly numbers, $12.5 million and $13.5 million (a Cy Young season between now and then would bump both to $16 million).

While Sale is the White Sox most valuable asset, Tanaka will be paid like an ace by whichever team he goes to, unless that winds up being the Dodgers, who downplay their chances to sign him, or the Tigers, who aren't known to be involved. Sale would actually become the third-highest paid starter on his team, as John Danks still has three years left on a sweetheart deal, but he's so unselfish that it's difficult to imagine him complaining about a contract that gave his young family financial security beyond its imagination.

Sale, owner of a 2.97 career ERA, would welcome Tanaka with open arms, no matter the difference in salaries and the attention they receive. With Adam Dunn's $15 million salary coming off the books at some point this year -- attempts to trade him have been unsuccessful -- it's easy to see a long-term fit for Tanaka, and it has to help that the $20 million posting fee can be paid in four installments, with $13.4 million due this year and $6.6 million next year.

The extent of Chicago's interest in Tanaka will largely depend on the results of the physical that agent Casey Close arranged for him to take on Thursday. The possible impact of high pitch counts (like the 160 he threw in his final Japan Series start) is a concern among scouts. It's also worth noting that his 1,315 career innings for the Rakuten Golden Eagles are the most for a 25-year-old since Frank Tanana blazed onto the scene as Nolan Ryan's wingman in the 1970s.

Tanana had to reinvent himself as a cerebral left-hander after he needed shoulder surgery in his age-25 season. It's no wonder that longtime White Sox trainer Herm Schneider (who along with pitching coach Don Cooper has an enviable record in keeping pitchers healthy) and the team's orthopedists will pore over results from an MRI and other tests.

Don't rule out the White Sox on Tanaka if they like his medical information. Like Abreu, he would demand that the Sox be taken seriously again, and under owner Jerry Reinsdorf, this has always been an organization that doesn't tolerate long stretches of rebuilding.

Phil Rogers is a columnist for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.